fade

Fading Cluster Structure and EMM Layer

Reduces the weight of old observations in the data stream.
build has a learning rate parameter
lambda. If this parameter is set, build automatically
fades all counts before a new data point is added. The second
mechanism is to explicitly call the function~fade whenever
fading is needed. This has the advantage that the overhead of manipulating
all counts in the EMM can be reduced and that fading can be used in a more
flexible manner. For example, if the data points are arriving at an irregular
rate, fade could be called at regular time intervals
(e.g., every second).

Usage

Arguments

learning rate. If lambda is missing,
the learning rate specified for the EMM is used.

Details

Old data points are faded by using a weight.
We define the weight
for data that is $t$ timesteps in the past by the following strictly
decreasing function:
$$w_t = 2^{-\lambda t}$$

Since the weight is multiplicative, it can be applied iteratively by
multiplying at each time step all counts by $2^-lambda$.
For the clustering algorithm the weight of the clusters (number of data
points assigned to the cluster) is faded. For the EMM the initial count vector
and all transition counts are faded.